Conservative descent for semi-orthogonal decompositions

Vortrag von Prof. Dr. Olaf Schnürer

Sprecher eingeladen von: Prof. Dr. Christian Okonek

Datum: 26.02.18  Zeit: 13.15 - 14.45  Raum: Y27H25

Motivated by the local flavor of several well-known semi-orthogonal decompositions in algebraic geometry, we introduce a technique called conservative descent, which shows that it is enough to establish these decompositions locally. The decompositions we have in mind are those for projectivized vector bundles and blow-ups (due to Orlov) and root stacks (due to Ishii and Ueda). Our technique simplifies the proofs of these decompositions and establishes them in greater generality for algebraic stacks. We may also discuss semi-orthogonal decompositions for families of Brauer-Severi varieties (due to Bernardara). This is joint work with Daniel Bergh (Copenhagen).